It looks like they use the photo as a height map. The lighter the pixel, the more to the front it is positioned. Portraits will have to be lighted equally, to prevent strange deforming (for instance when the face is partly in the shadow).

Lots of 3D software can generate an object with help of a height map / bump map and export an obj or 3ds file.

I think the secret is in the selection of the photo's. And no refund policy ('the result is as good as your photo').